On the state feedback diagonal decoupling of linear systems described by (A, B, C, E) quadruples
Antonis I. G. Vardulakis · International Journal of Control · 1981
Given a linear multivariable system σ = (A, B, C, E) giving rise to a proper but not strictly proper (m × m), non-singular, transfer function matrix T(a), this paper presents an alternative necessary and sufficient condition for the solvability of the diagonal decoupling and simultaneous pole assignment problem by the use of state feedback and input coordinate transformations using a polynomial matrix approach. The proof of the necessary and sufficient condition is constructive and apart from giving rise to a simple decoupling algorithm it can also be used in order to investigate the structure of the resulting closed-loop decoupled system.